### Abstract

Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m+r + b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

Original language | English (US) |
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Title of host publication | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |

Pages | 1-9 |

Number of pages | 9 |

State | Published - 2004 |

Event | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States Duration: Jun 9 2004 → Jun 11 2004 |

### Other

Other | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |
---|---|

Country | United States |

City | Brooklyn, NY |

Period | 6/9/04 → 6/11/04 |

### Fingerprint

### Keywords

- Geodesics
- Ham-sandwich
- Shortest paths
- Simple polygons

### ASJC Scopus subject areas

- Software
- Geometry and Topology
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)*(pp. 1-9)

**Geodesic ham-sandwich cuts.** / Bose, Prosenjit; Demaine, Erik D.; Hurtado, Ferran; Iacono, John; Langerman, Stefan; Morin, Pat.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04).*pp. 1-9, Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States, 6/9/04.

}

TY - GEN

T1 - Geodesic ham-sandwich cuts

AU - Bose, Prosenjit

AU - Demaine, Erik D.

AU - Hurtado, Ferran

AU - Iacono, John

AU - Langerman, Stefan

AU - Morin, Pat

PY - 2004

Y1 - 2004

N2 - Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m+r + b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

AB - Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m+r + b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

KW - Geodesics

KW - Ham-sandwich

KW - Shortest paths

KW - Simple polygons

UR - http://www.scopus.com/inward/record.url?scp=4544224052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544224052&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:4544224052

SP - 1

EP - 9

BT - Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)

ER -